Simulation of Brightness Temperatures for the Microwave
Radiometer (MWR) on the Aquarius/SAC-D Mission
Salman S. Khan
M.S. Defense
8th July, 2009
Outline
• Thesis Objective
• Aquarius Salinity Measurements
• Aquarius Radiometer/Scatterometer
• Microwave Radiometer (MWR)
• MWR Tb Simulation Requirements
• Yaw Steering Analysis
• Post-Launch Inter-Satellite Radiometric Calibration using WindSat
2
Thesis Objective
• Simulate realistic ocean brightness temperatures (Tb) for the 3-channel Microwave Radiometer (MWR) on Aquarius/SAC-D– To be used by CONAE for pre-launch
geophysical retrieval algorithms development
• Evaluate the proposed MWR measurement geometry and verify the requirements for spatial/temporal sampling
• Perform a preliminary study for the post-launch inter-satellite radiometric calibration using the WindSat radiometer as a reference
3
4
• Antenna
– Radiometer & Scatterometer share feeds and 2.5 m reflector
– Three footprints in pushbroom configuration
• Radiometer
– 1.413 GHz V, H-pol & 3rd Stokes
• Scatterometer
– 1.26 GHz H-pol
– Provides a critical correction for surface roughness
• Beams
– Inner – 76 x 94 Km
– Middle – 84 x 120 Km
– Outer – 96 x 156 Km
Aquarius Radiometer/Scatterometeron SAC-D
5
Microwave Radiometer (MWR) on SAC-D
• Radiometer
– Two radiometers
• 23.8 GHz (K band, V-pol)
• 36.5 GHz (Ka band, H, V-pol, +45o & -45o polarized output)
• All the polarizations are measured simultaneously
• Antenna
– Two Multi-beam parabolic-torus reflectors
• Forward & Aft looking beams
• 8 beams in push-broom configuration
• Two incidence angles, 52o & 58o
• IFOV Resolution of ~ 40 km
MWRMicrowave Radiometer
Aft-looking
Beams
Fwd-looking
Beams
6
MWR Forward Beam (Ka-Band) Geometry
7
•Satellite’s velocity along +X
•Only forward beams are shown
•Four beams @ 52o & four @ 58o EIA, alternating
MWR Fwd & Aft Beam Geometry
Conical Arc
Conical Arc
8
58o
EIA
52o
EIA90o
MWR beams are sequentially sampled in time
In 1.92 sec, the beams move along-track by 13.1 Km
1.92 sec
9
•The sampling time made the simulation very challenging
since the beams are sampled sequentially at 0.24 sec
intervals in which the spacecraft (and hence the footprint)
moves as well
MWR Tb Simulation Requirements
10
WindSat & MWR Sensor Geometry
WindSat Conical Scanning Radiometer MWR Pushbroom Radiometer 11
Why WindSat?
•Similar sun-synchronous orbits
•Similar frequency channels
•High resolution WindSat IDR
Conical Scanning Sensor Geometry
12
Conical Scanning Sensor Geometry cont.1
Antenna Beam IFOV
13
MWR Swath Width
14
Azimuthal Translation of MWR to Equivalent WindSat
15
Center of Earth
γ ct = 2.66o
γ ct = 5.58o
WindSat
MWR
ΔΨ WindSat
ΔΨ MWR
Satellite sub-track plane view
•Altitude WindSat = 840 Km
•Altitude MWR = 657 Km
•ΔΨ WindSat < ΔΨ MWR
MWR Swath Width
657 Km
840 Km
325.2 Km
Azimuthal Translation of MWR to Equivalent WindSat cont.
• MWR swath = 272 Km to 652 Km (to right of subtrack)
– corres ct = 2.66o to 5.58o
• Cross-track central angles ( ct) are the same for MWR and WindSat;
however central angles, () in the incident plane are different
– MWR 58 = 7.75°, 52 = 6.40°
– WindSat = 8.04o
• Using the equation,
solve for corresponding WindSat azimuth angles
Beam 1: Θ=52o
ψ=24.56o
Beam 8:Θ=58o
ψ=46.13o
sin ct sin sin
16
Beam-1
(Az, deg)
Beam-8
(Az, deg)
MWR 24.56 46.13
WindSat -19.37 -44.07
WindSat Azimuth Constraints
17
Longitude
La
titu
de
• 37 GHz azimuth range• Fwd: -50o to 53o
• Aft: 125o to 183o
• 23.8 GHz azimuth range• Fwd: -28o to 94o
• Aft: 142o to 211o
• For geophysical retrievals, forward and aft beams of MWR must be collocated
• Mirror the MWR swath on the left side, which offers sufficient common forward swath
WindSat Envir Data Record (EDR) Azimuth Constraints
• The EDR imposes a limit on the usable azimuth angles
• EDR azimuth range
-27.44o to 38.09o
• Left sided MWR mirrored swath will lose ~6o in azimuth; therefore swath is shifted to start from 38.09o
• Additional MWR beams generated using the entire azimuth range of EDR
18
-27.44o
38.09o
19.37o
44.06o
•Translated WindSat•EDR Azimuth Range
Flig
ht D
irection
WindSat EDR Azimuth Constraints• A total of 19 MWR beams
have been simulated
• 11 on the left & 8 on the right side of flight direction
• Left most MWR beam corresto swath width of 550.6 Km & right most corres to 411.1 Km
• The beam center to center swath spacing corres exactly to MWR spacing = 46.4 Km (325.2/ 7)
• Accurate spatial & sampling resolution of MWR
• Accurate orientation by change in azimuth
19
-27.44o38.09o EDR Azimuth Range
46.4 Km550.6 Km 411.1 Km
Flig
ht D
irection
•Beam Azimuth Angle:
γ ct = Swath width / ρ
Ψ beam= sin-1 (sin(γct)/sin(γ WindSat))
•The 8 beams on either side of flight direction are symmetrical by azimuth
58o EIA
52o EIA
53.8 54 54.2 54.4 54.6 54.8 55 55.2 55.4
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
Longitude
Latitu
de
23.8 GHz WindSat Intermediary Data Record
• High resolution spatial sampling along a conical scan
• Resolution 23 GHz - 12 x 20 Km
• Δψ 23.8 = 0.313o/pixel
20
54 54.2 54.4 54.6 54.8 55
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Longitude
Latitu
de
37 GHz WindSat Intermediary Data Record
• High resolution spatial sampling along a conical scan
• Resolution 37 GHz - 8 x 13 Km
• Δψ 23.8 = 0.21o/pixel21
Incidence Angle
Minor Axis (Km)
Major Axis(Km)
52o 28.5 46.3
58o 32 60.4
MWR IFOV Geometry
• MWR footprint dimensions
• Θ = 52o & 58o
• 3 dB beam width, β = 1.64o
• Slant range:
– R 58 = 1118.6 Km
– R 52 = 995.8 Km
Min
or
Axis
Major Axis
22
56.6 56.7 56.8 56.9 57 57.1 57.2 57.3 57.4
-4
-3.9
-3.8
-3.7
-3.6
-3.5
-3.4
LONGITUDE
LA
TIT
UD
E
56.6 56.7 56.8 56.9 57 57.1 57.2 57.3 57.4
-4
-3.9
-3.8
-3.7
-3.6
-3.5
LONGITUDE
LA
TIT
UD
E
52o
52o
58o
58o
37 GHz IDR Beam-Fill in MWR IFOV
• Number of along-scan IDR pixels falling into an elliptical footprint varies along ellipse major axis
• Complexity is reduced using a rectangular footprint
• Rectangular footprint has equal number of along-scan IDR pixels for all scans 23
23.8 GHz IDR Beam-Fill in MWR IFOV cont.
• The IDR pixels falling into a rectangular footprint, along-scan & along-track, are calculated with the following equations
• ‘n’ is the integer # of IDR pixels along-scan while ‘m’ is integer the # of IDR scans
56.6 56.7 56.8 56.9 57 57.1 57.2 57.3 57.4
-3.9
-3.8
-3.7
-3.6
-3.5
-3.4
LONGITUDE
LA
TIT
UD
E
23.8 GHz
1)/)(( xwMinorAxisn
1)/)(( ylMajorAxism
52o
58o
m = 3
n = 4n = 5
m = 4
l= 20 Km
w = 12 Km
x = 4.9 Km
y = 12.6 Km
23.8 GHz
Incidence Angle
Minor Axis (Km)
Major Axis(Km)
n m
52o 28.5 46.3 4 3
58o 32 60.4 5 4
24
56.4 56.6 56.8 57 57.2 57.4
-5.3
-5.2
-5.1
-5
-4.9
-4.8
LONGITUDE
LA
TIT
UD
E
37 GHz IDR Beam-Fill in MWR IFOV cont.
37 GHz
52o
58o
m = 5
m = 4
n = 8n = 7
l = 13 Km
w = 8 Km
x = 3.3 Km
y = 12.6 Km
37 GHz
• The IDR pixels falling into a rectangular footprint, along-scan & along-track, are calculated with the following equations
• ‘n’ is the integer # of IDR pixels along-scan while ‘m’ is the integer # of IDR scans
1)/)(( xwMinorAxisn
1)/)(( ylMajorAxism
Incidence Angle
Minor Axis (Km)
Major Axis(Km)
n m
52o 28.5 46.3 7 4
58o 32 60.4 8 5
25
IDR Scan Mapping into MWR Pixels
• MWR Inter-scan distance = 13.1 Km
• IDR Inter-scan distance = 12.6 Km
• Difference = 0.5 Km; therefore periodically an IDR scan will be skipped
• This period is 12.6 Km/0.5 Km = 25.2 scans
12.6 Km
13.1 Km
IDR Scan skipped
26
Successive
MWR Scans
MWR IFOV Summary
Frequency Incidence Angle Width (Km) Length (Km) IDR Pixels n
(Across Track)
IDR Scans m
(Along Track)
23.8 GHz 58o 31.6 57.8 5 4
52o 26.7 45.2 4 3
37 GHz 58o 31.1 63.4 8 5
52o 27.8 50.8 7 4
56.6 56.7 56.8 56.9 57 57.1 57.2 57.3 57.4
-3.9
-3.8
-3.7
-3.6
-3.5
-3.4
LONGITUDE
LA
TIT
UD
E
23.8 GHz
52o
58o
m = 3
n = 4n = 5
m = 4
56.4 56.6 56.8 57 57.2 57.4
-5.3
-5.2
-5.1
-5
-4.9
-4.8
LONGITUDE
LA
TIT
UD
E
37 GHz
52o
58o
m = 5
m = 4
n = 8n = 7
27
MWR Pixel Collocations
50 51 52 53 54 55 56 57 58 59 60 61-8
-7.5
-7
-6.5
-6
-5.5
-5
-4.5
-4
-3.5
-3
Longitude
Latitu
de
Longitude
Latitu
de
Collocated 23.8 (Green) & 36.5 (Red) GHz Beams
Orientation
by Azimuth
28
52o
58o
Scan # n
Scan # n + 6
Scan # n + 12
MWR 37 GHz Pixels
54 56 58 60 62 64
-25
-24.5
-24
-23.5
-23
-22.5
-22
-21.5
-21
-20.5
-20
Longitude
Latitu
de
MWR 36.5 GHz Swath at 58o (Red) & 52o (Green)
IDR Scan
Skip
IDR Scan
Skip
~ 25 scans
29
30
Start
WindSat IDR file
Filter out skipped IDR scans
Filtered WindSat IDR file
Filter WindSat IDR File
Beam 1…19 (θ, f, ψ)
Calculate Beam m, n (θ, f)
Find the along-scan IDR pixels(n, ψ)
Find the along-track range of scans(m)
Average Tb of IDR pixels
Average Tb of MWR Beams
MWR IFOV Summary
Get IDR Scan
Last scan?
No
Yes
MWR Tb
File
Store 19 MWR Beams of the scan
Comparison of WindSat & MWR Tb at 37 GHz (V-pol) @ 53 deg
100 200 300 400 500 600 700
100
200
300
100 200 300 400 500 600 700
100
200
300
200
250
300
200
250
300
WindSat Tb
MWR Tb
31
• 0.50 resolution
• Tb average of 68
obits in Feb 2007
• Shows radiometric
accuracy of the Tb
simulation
• Mean ΔTb = 0 K
• σ ΔTb = ~2 K
Tb Normalization
• WindSat Tb normalizations are required for incidence angle & frequency adjustment
– WindSat operates at 23.8 - & 37-GHz @ 53°
– MWR operates at 23.8 - & 36.5-GHz @ 52°& 58o
• Radiative Transfer Model (RTM) was used to transform WindSat Tb measurements to equivalent MWR frequencies and incidence angles
32
WindSat Normalization Procedure
• Run RTM
– Calculate theoretical MWR Tb for environmental parameters (1°box)
• Tb (MWR-perdicted)(fMWR,ƟMWR, WS,SST,WV,CLW )– Frequency = 23.8- & 36.5 GHz
– Incidence angle = 52˚ & 58˚
– Calculate theoretical WindSat Tb for environmental parameters (1°box)
• Tb(WS-perdicted)(fWS,ƟWS, WS,SST,WV,CLW)– Frequency = 23.8- & 37 GHz
– Incidence angle = 53˚
33
Expected Delta Tb (MWR to WindSat)
– Calculate the predicted (theoretical) Tb difference between MWR & WindSat
• delta = MWR predicted – WS predicted
Tb MWR = WindSat (measured) + delta
34
180 190 200 210 220 230 240 250 260
200
210
220
230
240
250
260
WindSat Tb (K)
MW
R T
b (
K)
Tb Normalization of 23.8 V Channel (58o)
45o Line
2nd order
regression
WindSat Tb(K)
MW
R T
b(K
)
35
WindSat Tb (K)
MW
R T
b (
K)
180 190 200 210 220 230 240 250 260
200
210
220
230
240
250
260
MW
R T
b(K
)
WindSat Tb(K)
MW
R T
b(K
)
•Ran RTM for 1 week to calculate WindSat & MWR theoretical Tb s
•Tb (theoretical) ( f, Ɵ, WS,SST,WV,CLW ), envr. parameters from GDAS
•Tb normalizations were done for all channels (23.8 V, 36.5 V & H) at 52o &
58o incidence angles
•The Tb Biases were found to be independent of the environmental
variables
Yaw Steering Results
Yaw Direction
Flig
ht D
irection
Flig
ht D
irection
Y
Z
Y
Z
Aquarius/SAC-D Yaw Steering
Aquarius/SAC-D Yaw Steering
-100 -80 -60 -40 -20 0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3
3.5
4
Latitude
Absolu
te Y
aw
(D
egre
es)
Absolute Yaw as a function of
Latitude (Provided by CONAE)Collocated MWR & Aquarius Swath
Earth’s Rotation
38
Latitude
Absolu
te Y
aw
(D
eg)
Max Yaw at Equator
Min Yaw at Poles
Evaluation Procedure
• Used STK to simulate SAC-D orbit (Inclination 98o,Eccentricity = 0, Altitude = 657 Km) & generated:
– SSPs
– Satellite Velocity Azimuth (relative to North)
– @ 0.24 sec time step
• Generated corresponding pairs of forward/aft beam points sequentially for 8 pairs@ 0.24 sec step, using:
– SubSat Point (SSP) (lat, lng)
– Earth Central Angle (γ) b/w SSP & beam boresight
– Beam Compass Azimuth (+ Yaw @ SSP_lat)
39
Evaluation Procedure cont.
Satellite Velocity Azimuth40
Beam Compass Azimuth Angle for Ascending Flight
Beam (yawed)
Beam (without yaw)
Yaw
Sub-satellite point
0o Lat
Velocity Compass Az Angle
(SV_CAA)
Beam Azimuth
(Beam_Az)
Beam Azimuth with
Yaw (Beam_Az_Yaw)
Beam_CAA_Yaw = modulo ((SV_CAA + Beam_Az + Yaw), 360)
Earth’s Rotation
North
41
Beam Compass Azimuth Angle for Descending Flight
Beam (yawed)
Beam (without yaw)
Sub-satellite point
0o Lat
Velocity Compass Az Angle
(SV_CAA)Beam Azimuth
(Beam_Az)
Beam Azimuth with
Yaw (Beam_Az_Yaw)
Earth Rotation
North
42
Beam_CAA_Yaw = modulo ((SV_CAA + Beam_Az + Yaw), 360)
BEAM 1 ASC.
BEAM 1 DSC.
BEAM 8 ASC.
BEAM 8 DSC.
Beam-1 separation = 6 km Beam-8 separation = 2.2 km
Beam-8 separation = 6.1 km Beam-1 separation = 6 km
43
Forward/Aft Beam-1 Collocation Separation
Mean ~4 Km
Latitude
44
Collo
cation S
epara
tion (
Km
)•ASC
•DSC
Forward/Aft Beam-8 Collocation Separation
Dis
tance (
Km
)
Mean ~4.1 Km
Latitude
45
Collo
cation S
epara
tion (
Km
)•ASC
•DSC
A Snapshot of 3 Forward Beams Collocating
-64 -62 -60 -58 -56 -54 -52 -50 -48
28
30
32
34
36
38
Longitude
Latitu
de Fwd
Beams
Aft
Beams
46
Aft
Beams
Collocation
Collocation
All Forward Beams Collocating withDifferent Aft Scans
47
-68 -66 -64 -62 -60 -58
55
56
57
58
59
Longitude
Latitu
de
Fwd Scan # 437
Aft Scan #:
Aft Scan #:536
558
529
552
519
543
504
530
Post-launch Inter-Satellite Radiometric Calibration using WindSat
48
WindSat shares similarities in orbit (ground track), radiometer frequencies and swath overlap with MWR
Parameter WindSat MWR
Altitude 840 Km 657 Km
Eccentricity 0.00134 0.0012
Inclination Angle 98.7o 98.01o
Ascending Node 6 p.m. 6 p.m.
Frequency23.8 (V & H) and 37.0 (V & H)
23.8 (V) and 36.5 (V & H) GHz
Swath Width ~950 Km ~380 Km
Earth Incidence Angle
53o 52o & 58o
49
50
Phased in
Phased out
• Aquarius speed > Coriolis & it laps in ~45 hours and 36 mins • During half of this period, satellite ground tracks are out of phase•Time for satellite ground tracks to be coincident (in phase at same Lat/Lng) is ~57 days
51
ASC/DSC Collocations (0.5o resolution)
52
Ascending Collocations
DescendingCollocations
• Approx 19,000 collocations in 45 hrs (± 50o Lat)• (0.5o x 0.5o) & ± 45 min window
• Approx 1 Million ocean collocations in 5 months
53
Conclusions
• The MWR Tb simulation is validated to have radiometric and temporal/spatial accuracy
• CONAE’s yaw steering technique to collocate the forward & aft MWR beams has also been verified with a mean collocation separation ~ 4 Km
• The inter-satellite swath collocation between WindSat and MWR shows that ~5 months in orbit, there will be ~1 Million ocean collocations
54
Future Work
• A four month simulated Tb dataset for the 3-channel MWR will be delivered to CONAE for the pre-launch geophysical retrieval algorithms development
• The MWR retrievals will be validated through near simultaneous, collocated comparisons with WindSat’s Environmental Data Records (EDRs)
55
Backup Slides
57
58
Best-Fit Gaussian
Gaussian fit for Bin # 5 of Wind Speed Bias
-30 -25 -20 -15 -10 -5 0 5 10 15 200
100
200
300
400
500
600
700
Bias bins
Fre
quency o
f occure
nce
Outliers Outliers
59